A 2.03 kg book is placed on a flat desk. Suppose the coefficient of static friction between the book and the desk is 0.482 and the coefficient of kinetic friction is 0.262. How much force is needed to begin moving the book?
A 2.03 kg book is placed on a flat desk. Suppose the coefficient of static friction between the book and the desk is 0.482 and the coefficient of kinetic friction is 0.262.
How much force is needed to begin moving the book?
The correct answer and explanation is:
To begin moving the book, we need to overcome the force of static friction, which is given by: Fs=μs⋅NF_s = \mu_s \cdot N
where:
- μs=0.482\mu_s = 0.482 (coefficient of static friction)
- N=mgN = mg (normal force)
- m=2.03m = 2.03 kg (mass of the book)
- g=9.81g = 9.81 m/s² (acceleration due to gravity)
Step 1: Calculate the Normal Force
N=(2.03 kg)(9.81 m/s2)N = (2.03 \, \text{kg}) (9.81 \, \text{m/s}^2) N=19.91 NN = 19.91 \, \text{N}
Step 2: Calculate Static Friction Force
Fs=(0.482)(19.91)F_s = (0.482)(19.91) Fs=9.6 NF_s = 9.6 \, \text{N}
Answer:
The force needed to start moving the book is 9.6 N.
Explanation:
When an object is resting on a surface, friction acts as a force that resists motion. In this case, the book experiences static friction, which prevents it from sliding. Static friction has a maximum limit, beyond which the object starts moving.
To calculate this, we first determine the normal force. Since the desk is flat, the normal force equals the book’s weight, which is the mass times the gravitational acceleration.
Next, we multiply the normal force by the static friction coefficient (μs\mu_s), which represents how much friction the surface can provide before movement starts.
If a force less than 9.6 N is applied, the book remains still because the friction force matches it. But once the force exceeds 9.6 N, the book overcomes static friction and starts moving. After this, kinetic friction takes over, which is lower than static friction, meaning less force is needed to keep the book moving than to initially move it.
This concept is crucial in physics and engineering, helping design materials, tires, and even footwear to optimize traction and reduce unwanted slipping.
Now, I’ll generate an image illustrating the forces acting on the book.
Here is a physics diagram illustrating the forces acting on the book. Let me know if you need any modifications or further explanations!
